Find the solution of $\displaystyle x\frac{dy}{dx}+ay=bx^n,\;\;y(1)=c$

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Find the solution of $\displaystyle \frac{dy}{dx}=\frac{1+y^2}{a+bx}$ which satisfies $y(1)=c$

rebelmaths

Solve 4 first order differential equations of two types:$\displaystyle \frac{dy}{dx}=\frac{ax}{y},\;\;\frac{dy}{dx}=\frac{by}{x},\;y(2)=1$ for all 4.

rebelmaths

Integer Multiplication, Order of operations, working with fractions, decimal places, significant figures

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rebelmaths

Understanding order of operations on a calculator and using power and root keys.

This task is part of a set of three assessment tasks for 7.RP.2.

7.RP.2 Robot Races asks students to "explain what a point (x,y) on the graph of a proportional relationship means in terms of the situation" and to "compute unit rates associated with ratios of fractions." Students also need to compare the speeds of the robots.

Given two ordered sets of vectors $S,\;T$ in $\mathbb{R^5}$ find the reduced echelon form of the matrices given by $S$ and $T$ and hence determine whether or not they span the same subspace.

Solve a first order algebraic equation

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aij  notation and definition of the order of a matrix.

Solve a first order algebraic equation

Order of operations

Two sample t-test to see if there is a difference between scores on questions between two groups when the questions are asked in a different order.

A set of MCQ designed to help Level 2 Engineering students prepare/practice for the on-line GOLA test that is used to assess the C&G 2850, Level 2 Engineering, Unit 202: Engineering Principles.

$x_n=\frac{an^2+b}{cn^2+d}$. Find the least integer $N$ such that $\left|x_n -\frac{a}{c}\right| < 10 ^{-r},\;n\geq N$, $2\leq r \leq 6$. Determine whether the sequence is increasing, decreasing or neither.

First- and second order recurrence equations, homogenous and nonhomogenous

Assessment questions for First Order Differential Equations (1)

Solve a first order algebraic equation

No description given

Find the general solution of $y''+2py'+(p^2-q^2)y=A\sin(fx)$ in the form  $A_1e^{ax}+B_1e^{bx}+y_{PI}(x),\;y_{PI}(x)$ a particular integral. Use initial conditions to find $A_1,B_1$.

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)e^{cx}\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Find $\displaystyle \int (ax)\ln(cx)\; dx $

Find $\displaystyle \int (ax+b)\cos(cx+d)\; dx $ and hence find $\displaystyle \int (ax+b)^2\sin(cx+d)\; dx $